Interferometric optical techniques are widely used to measure optical thickness, flatness, and other geometric and refractive index properties of precision optical components such as glass substrates used in lithographic photomasks. For example, to measure the surface profile of a measurement surface, one can use an interferometer to combine a test wavefront reflected from the test surface with a reference wavefront reflected from a reference surface to form an optical interference pattern. The test wavefront and the reference wavefront, typically from a common light source, travel over different optical paths to their respective surfaces and then onto a camera where they form an interference pattern. The difference between the lengths of those optical paths determine an optical path difference (OPD) between the test and reference wavefronts at the optical interference pattern. Spatial variations in the intensity profile of the optical interference pattern correspond to phase differences between the combined test and reference wavefronts caused by variations in the profile of the test surface relative to the reference surface.
Phase-shifting interferometry (PSI) can be used to accurately determine the phase differences between the wavefronts and the corresponding profile of a test surface. With PSI, the optical interference pattern is recorded for each of multiple phase-shifts between the reference and test wavefronts to produce a series of optical interference patterns that span at least a full cycle of optical interference (e.g., from constructive, to destructive, and back to constructive interference). For each optical interference pattern in the series, a detector or camera records intensity values over a lateral spatial region. For each lateral spatial location or “pixel”, the series of interference patterns defines a series of intensity values or “interferogram” which has a sinusoidal dependence on phase-shifts producing fringes in the interferogram. Each interferogram is a sinusoid with a phase-offset equal to the phase difference between the combined test and reference wavefronts for that pixel location. Using numerical techniques known in the art, the phase-offset for each spatial location is extracted from the fringes in the interferograms to provide a profile of the test surface relative the reference surface. Such numerical techniques are generally referred to as phase-shifting algorithms.
The phase-shifts in PSI can be produced by changing the optical path length from the test surface to the interferometer relative to the optical path length from the reference surface to the interferometer. For example, the test surface can be moved relative to the reference surface, changing the OPD. An interferogram spanning a full cycle of optical interference can be produced by scanning the OPD over a full wavelength of the common light source. It is therefore unnecessary to scan the OPD over a distance larger than a couple of wavelengths in PSI.
Interferometers using PSI are particularly well-suited for measuring nominally flat surfaces. For example, a single-wavelength visible interferometer using phase-shifting techniques can measure surface variations on the order of Angstroms. Such accuracy is important in applications such as characterizing of glass substrates used in lithographic photomasks. However, for rough surface profiles with step discontinuities or features larger than a wavelength PSI may suffer from impairments due to 2π phase ambiguities.
Another type of interferometer is a broadband scanning interferometer, which uses a broadband source and scans the OPD between the reference and test paths of the interferometer. Because the broadband source has a limited coherence length, interference fringes in the interferogram are only present where the OPD between the test and reference paths for corresponding points on the test surface and the flat reference surface is less than the coherence length. The fringes in the interferogram are localized within a coherence envelope. Thus, the scanning interferometer can resolve a step, or an otherwise large and/or discontinuous, variation in the surface of interest by scanning the OPD, recording multiple interferograms, and determining for each pixel which OPD values produce fringes in the interferogram. This localization of fringes is not impaired by 2π phase ambiguities. For a simple reflective surface the coherence envelope has a single peak at zero-OPD. Therefore, in contrast to PSI, broadband scanning interferometry typically scans the OPD over a distance larger than a wavelength in order to scan over a range of height variation in the test surface. See, e.g., N. Balasubramanian in U.S. Pat. No. 4,340,306 and P. de Groot in U.S. Pat. No. 6,195,168 for additional information regarding scanning interferometers. Such broadband scanning interferometry may be thought of as an example of “low-coherence scanning interferometry.”